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CN111272883A - Rock fracture mode intelligent detection and identification method based on acoustic emission model - Google Patents

Rock fracture mode intelligent detection and identification method based on acoustic emission model Download PDF

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CN111272883A
CN111272883A CN202010144388.8A CN202010144388A CN111272883A CN 111272883 A CN111272883 A CN 111272883A CN 202010144388 A CN202010144388 A CN 202010144388A CN 111272883 A CN111272883 A CN 111272883A
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朱星
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Chengdu Univeristy of Technology
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Abstract

The invention discloses an intelligent detection and identification method for a rock fracture mode based on an acoustic emission model, which comprises the following steps: the method comprises the steps of firstly arranging an acoustic emission system for testing acoustic emission parameters of a rock cracking process on a rock to be monitored, then inputting target characteristic data into a pre-trained signal recognition model, obtaining the signal recognition model through training of a rock cracking acoustic emission training set in advance, then intelligently recognizing the proportion of tension and shear crack development in the rock cracking process, and finally recognizing that corresponding relations exist between waveform characteristics determined according to the rock cracking acoustic emission signals and rock cracking patterns, so that a series of reliable detection threshold values are provided for quantitatively formulating a rock disaster early warning scheme, and an analysis method is provided for deeply researching and recognizing rock cracking instability precursor signal characteristics.

Description

Rock fracture mode intelligent detection and identification method based on acoustic emission model
Technical Field
The invention relates to the technical field of geological survey application, in particular to an intelligent detection and identification method for a rock fracture mode based on an acoustic emission model.
Background
The acoustic emission signal detection technology provides an attractive solution for damage evaluation/structural health monitoring of various rock structures (slopes, dams, roadbeds, tunnels and the like). The performance and functionality of these civil structures is related to social security, and in all types of natural events (i.e., earthquakes, hurricanes, and tsunamis), these events may compromise their security and usability. To ensure the overall stability of these structures, it is important, especially in engineering practice, to correctly assess and predict the development of rock fractures, since the model of rock fractures reflects not only its condition as a material, but also the condition of the entire system at the structural level.
Acoustic Emission (AE) based methods provide an attractive solution for the nucleation and propagation of cracks in rock structures. The invention provides an intelligent detection and identification method of a rock fracture mode based on a Gaussian Mixture Model (GMM), which is a non-supervision classification technology based on distribution, and is successfully applied to a plurality of fields, including voice identification, image processing, dynamic systems, tracking and text identification; however, this technique has not been used for intelligent identification of rock fracture patterns based on acoustic emissions. Based on the reasons, a rock fracture mode classification probability scheme based on an acoustic emission Gaussian mixture model is provided.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides an intelligent rock fracture mode detection and identification method based on an acoustic emission model.
In order to realize the purpose of the invention, the invention provides the following technical scheme:
an intelligent detection and identification method for rock fracture modes based on an acoustic emission model comprises the following steps:
step 1, arranging an acoustic emission system for testing acoustic emission parameters in a rock breaking process on a rock to be monitored;
step 2, inputting acoustic emission parameters collected by an acoustic emission system in the rock breaking process into a pre-trained signal recognition model, wherein the signal recognition model is obtained by pre-training a training set of rock breaking acoustic emission;
step 3, intelligently identifying the development proportion of tension and shear cracks in the rock cracking process by a signal identification model;
and 4, according to the relation between the waveform characteristics determined by the rock cracking acoustic emission signals and the rock cracking mode identification, providing a series of reliable detection threshold values for quantitatively formulating a rock disaster early warning scheme, and simultaneously providing an analysis method for deeply researching and identifying rock cracking instability precursor signal characteristics.
Preferably, in step 1, the acoustic emission system selects the ringing count, duration, peak frequency and rise time in the rock acoustic signal for analysis of the rock fracture process.
Preferably, in step 1, the method for acquiring rock acoustic signals by the acoustic emission system is based on JCMS parametric analysis:
calculating average frequency A of acoustic emission parameter by ringing count/durationFUsing the rise time/peak amplitude to obtain RAThe two sets of data are then sorted.
Preferably, in step 2, the preset training set of the signal recognition Model includes a Gaussian Mixture Model (GMM) and an Expectation Maximization (EM) algorithm.
Preferably, in step 2, according to AFAnd RAThe relation between the model and the model is used for analyzing tension and shear cracks, when tension and shear crack analysis is carried out, a Gaussian mixture model and an expected maximum algorithm are combined to serve as training models, the probability value of sampling and the closeness degree of the probability value of the model are observed to judge whether the model is fit or good, and the A is compared with the AFAnd RAThe relationship between them is intelligently detected and identified.
Preferably, in step 2, the process is iteratively repeated several times by adjusting the model to make the new model more adaptive to the probability values, and stopping updating and completing model training until the two probability values are very close, and the process is implemented by an algorithm:
calculating expected values of data through a Gaussian mixture model, wherein the Gaussian mixture model is a parameter probability density function and is expressed as weighting of Gaussian density of M components, and the expected values are maximized by continuously iterating to update the mean value mu and the standard deviation sigma of distribution until the two parameters change very little;
for D-dimensional measurement, training, the mixture density is defined as:
Figure BDA0002400222810000021
in the formula, ωiIn order to mix the weight values, the user can select the weight value,
Figure BDA0002400222810000022
is a single mode gaussian (normal) density,
Figure BDA0002400222810000023
is a feature vector;
the gaussian component density of each single mode is in the form of a D-variant gaussian function:
Figure BDA0002400222810000024
in the formula (I), the compound is shown in the specification,
Figure BDA0002400222810000025
the vector is an average vector of Dx1, and the sigma i is a covariance matrix of DxD;
to let the mixed weight omegaiSatisfy the requirement of
Figure BDA0002400222810000026
The complete Gaussian mixture model should be formed by averaging vectors
Figure BDA0002400222810000027
Covariance matrix
Σ i and the mixed weighting of all component densities M to parameterize it λ, which is expressed by equation (3):
Figure BDA0002400222810000028
for a classification system based on a Gaussian mixture model, the goal of model training is to estimate the lambda of the parameters of the Gaussian mixture model so that the Gaussian mixture density and the feature vector
Figure BDA0002400222810000029
Determining the optimal estimate of λ;
maximum Likelihood estimation (ML) is used to estimate ωi
Figure BDA00024002228100000210
And Σ i, the maximum likelihood estimation estimate maximizes the probability of a gaussian mixture model given the training data, for a series of T training vectors
Figure BDA0002400222810000031
Given the independence between vectors, can be written as
Figure BDA0002400222810000032
Since this expression is computationally intractable for direct maximization (i.e. setting the first derivative equal to zero and constraining the second derivative to be positive) as a non-linear function of λ, it is considered to obtain the ML parameter by iteration of an Expectation-maximization algorithm (EM for short).
Preferably, in step S2, the training process of the expectation-maximization algorithm is an iterative process, starting from the initial model λkInitially, a new model λ is then estimatedk+1Thus, there is p (X | λ)k+1)>p(X|λk) So that the new model becomes the initial model for the next iteration and the process is repeated until a certain convergence threshold is reached (e.g. the log likelihood is 1026), the algorithm consisting of two steps of expectation and maximization, which ensures a monotonic increase in the model's belief value, the result of the expectation step being the posterior probability for the i-th component, which is defined as the probability of state i, when the m-th mixture of gaussians results in state i
Figure BDA00024002228100000311
Given the kth re-estimated model λk
Figure BDA00024002228100000310
In the formula (I), the compound is shown in the specification,
Figure BDA0002400222810000033
the distribution parameters are returned by equations (6), (7) and (8), respectively, with a maximization step:
Figure BDA0002400222810000034
Figure BDA0002400222810000035
Figure BDA0002400222810000036
the gaussian mixture model can classify structures having two types of crack patterns, i.e., tensile crack and shear crack (M is 2), such as rock and concrete, and the feature vector is used to classify the two types of crack patterns
Figure BDA0002400222810000037
(or measurement vector) is considered to be a two-dimensional vector (i.e., a vector of measurements)
Figure BDA0002400222810000038
) When there are T training vectors, the sequence
Figure BDA0002400222810000039
The two classes correspond to the pull and shear modes I ═ 1, 2, respectively, at which point the parameters of the gaussian mixture model (weight, mean and covariance matrices for each hidden class) are "estimated" and matched to the training eigenvectors
Figure BDA0002400222810000041
Are most closely matched.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides an intelligent detection and identification method of a rock fracture mode based on an acoustic emission model, which provides a solution for the disaster types of sudden brittle fracture of rock masses such as rock collapse, rock landslide and the like, breaks through the objective limitations of poor real-time performance, insufficient precursors, low success rate and the like of the traditional method for indirectly monitoring damage and damage of rock masses and realizing early warning by deformation, solves the technical approach of effective monitoring and early warning of sudden brittle and unstable rock mass damage disasters, provides effective scientific support for disaster prevention and reduction and emergency disaster relief of large-scale rock mass damage disasters (rock collapse, rock fall and landslide), and has very important scientific significance and application value.
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Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a rock crack classification diagram;
FIG. 2 shows stress σ of limestone under uniaxial compressioncCrack identification results in the early stage and the middle and later stages;
FIG. 3 is a table of the percentage stress interval for limestone tension and shear cracks;
fig. 4 shows the proportion of the two cracks of the limestone in each loading stage.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments.
An intelligent rock fracture mode detection and identification method based on an acoustic emission model specifically comprises the following steps:
step 1, arranging an acoustic emission system for testing acoustic emission parameters in a rock breaking process on a rock to be monitored;
in step 1, the acoustic emission system selects the ringing count, duration, peak frequency and rise time in the rock acoustic signal for analysis of the rock fracture process.
In step 1, the method for acquiring rock acoustic signals by the acoustic emission system is based on a JCMS parameter analysis method:
calculating average frequency A of acoustic emission parameter by ringing count/durationFUsing the rise time/peak amplitude to obtain RAThe two sets of data are then sorted.
Step 2, inputting target characteristic data into a pre-trained signal recognition model, wherein the signal recognition model is obtained by training a training set of rock fracture acoustic emission in advance;
in step 2, the preset training set of the signal recognition model includes a Gaussian Mixture Model (GMM) and an Expectation Maximization (EM) algorithm.
In step 2, according to AFAnd RAThe relation between the model and the model is used for analyzing tension and shear cracks, when tension and shear crack analysis is carried out, a Gaussian mixture model and an expected maximum algorithm are combined to serve as training models, the probability value of sampling and the closeness degree of the probability value of the model are observed to judge whether the model is fit or good, and the A is compared with the AFAnd RAThe relationship between them is intelligently detected and identified.
In step 2, the new model is adapted to the probability value by adjusting the model, the process is iterated for many times until the two probability values are very close to each other, the updating is stopped and the model training is completed, and the process is realized by an algorithm:
calculating expected values of data through a Gaussian mixture model, wherein the Gaussian mixture model is a parameter probability density function and is expressed as weighting of Gaussian density of M components, and the expected values are maximized by continuously iterating to update the mean value mu and the standard deviation sigma of distribution until the two parameters change very little;
for D-dimensional measurement, training, the mixture density is defined as:
Figure BDA0002400222810000051
in the formula, ωiIn order to mix the weight values, the user can select the weight value,
Figure BDA0002400222810000052
is a single mode gaussian (normal) density,
Figure BDA0002400222810000053
is a feature vector;
the gaussian component density of each single mode is in the form of a D-variant gaussian function:
Figure BDA0002400222810000054
in the formula (I), the compound is shown in the specification,
Figure BDA0002400222810000055
the vector is an average vector of Dx1, and the sigma i is a covariance matrix of DxD;
to let the mixed weight omegaiSatisfy the requirement of
Figure BDA0002400222810000056
The complete Gaussian mixture model should be formed by averaging vectors
Figure BDA0002400222810000057
Covariance matrix
Σ i and the mixed weighting of all component densities M to parameterize it λ, which is expressed by equation (3):
Figure BDA0002400222810000058
for a classification system based on a Gaussian mixture model, the goal of model training is to estimate the lambda of the parameters of the Gaussian mixture model so that the Gaussian mixture density and the feature vector
Figure BDA0002400222810000059
Determining the optimal estimate of λ;
maximum Likelihood estimation (ML) is used to estimate ωi
Figure BDA00024002228100000510
And Σ i, the maximum likelihood estimation estimate maximizes the probability of a gaussian mixture model given the training data, for a series of T training vectors
Figure BDA00024002228100000511
Given the independence between vectors, can be written as
Figure BDA00024002228100000512
Since this expression is computationally intractable for direct maximization (i.e. setting the first derivative equal to zero and constraining the second derivative to be positive) as a non-linear function of λ, it is considered to obtain the ML parameter by iteration of an Expectation-maximization algorithm (EM for short).
In step S2, the training process for the expectation maximization algorithm is an iterative process, starting from the initial model λkInitially, a new model λ is then estimatedk+1Thus, there is p (X | λ)k+1)>p(X|λk) So that the new model becomes the initial model for the next iteration and the process is repeated until a certain convergence threshold is reached (e.g. the log likelihood is 1026), the algorithm consisting of two steps of expectation and maximization, which ensures a monotonic increase in the model's belief value, the result of the expectation step being the posterior probability for the i-th component, which is defined as the probability of state i, when the m-th mixture of gaussians results in state i
Figure BDA0002400222810000061
Given the kth re-estimated model λk
Figure BDA0002400222810000062
In the formula (I), the compound is shown in the specification,
Figure BDA0002400222810000063
the distribution parameters are returned by equations (6), (7) and (8), respectively, with a maximization step:
Figure BDA0002400222810000064
Figure BDA0002400222810000065
Figure BDA0002400222810000066
the GMM can classify structures having two types of crack patterns, i.e., tensile and shear crack patterns (M2), such as rock and concrete, and classify the two types of crack patterns by using eigenvectors
Figure BDA0002400222810000067
(or measurement vector) is considered to be a two-dimensional vector (i.e., a vector of measurements)
Figure BDA0002400222810000068
) When there are T training vectors, the sequence
Figure BDA0002400222810000069
The two classes correspond to the pull and shear modes I ═ 1, 2, respectively, at which time the parameters of the GMM (weight, mean and covariance matrices for each hidden class) are "estimated" and matched to the training eigenvectors
Figure BDA00024002228100000610
Are most closely matched.
Step 3, intelligently identifying the proportion of tension to shear crack development in the rock cracking process, as shown in figure 1;
and 4, according to the corresponding relation between the waveform characteristics determined by the rock cracking acoustic emission signals and the rock cracking mode identification, providing a series of reliable detection threshold values for quantitatively formulating a rock disaster early warning scheme, and simultaneously providing an analysis method for deeply researching and identifying rock cracking instability precursor signal characteristics.
Example 1
The whole training can be summarized as follows:
① initializing the parameters in lambda, and preliminarily determining two coded parameters of Gaussian mixture under state correlation by using a vector quantization method;
② obtaining Pr (i | x) by applying formula (5)t,λk);
③ use Pr (i | x)t,λk) To better estimate the parameter lambdak+1(see formulae (6) to (8));
④ iterates through steps ② and ③ until convergence.
As shown in FIG. 2, (a) and (b) are stress σ of limestone under uniaxial compressioncAnd (5) intelligent crack identification results in the initial stage and the middle and later stages. From the figure, it can be observed that the limestone is (0-0.1) sigma at the initial loading stagecAlmost all the tension cracks are tension cracks, the ellipse of tension clustering is round, the point dispersion around the central point is more average, and the sigma is loaded to the middle step (0.5-0.6)cThe transition stage from stretching to shearing is developed, and A is under the action of a large loadFUsually of higher amplitude, so RAThe value is changed in a small range, the clustering high-probability area gradually moves to the mean value range of the cut class, two mutually exclusive classifications (cutting and stretching) start to gradually form confluence (mixing), but the two classifications are still segmented, and at the stage, the high-probability area is almost completely concentrated near the mean value of the cut class.
The method is well applied to indoor uniaxial compression and acoustic emission tests, the percentage of the limestone tension cracks and the shear cracks in the whole loading stage is shown in figure 3, the percentage of the shear cracks in 80% -90% of the total loading time is found to reach the maximum value, and at the moment, a rock sample enters the later stage of an unstable expansion stage. In this study, the maximum percentage of limestone shear cracks was 44.59%, which was used as a prognostic threshold for limestone failure prediction, and when the percentage exceeded this threshold, an early warning was triggered as a prognosis of severe rock damage. R of two failure crack type cluster center positions simultaneouslyAAnd AFHas a shear crack low of AFHigh RAAcoustic emission signal characteristic of value, tensile crack having high AFAnd low RACharacterization of the values, this being in comparison with the R of the tensile and shear cracks obtained by JCMS parametric analysisAAnd AFCharacteristics of valueAs such.
Finally, in order to verify the classification results of the cracks in all loading steps, FIG. 4 shows the proportion of acoustic emission activities associated with two crack clusters in the limestone during each loading step, the limestone can be found to play a dominant role in tensioning the cracks in the whole loading process, namely most acoustic emission signals are generated by the nucleation of the tensioned cracks, the crack failure mode of the acoustic emission test in the rock chamber is not obviously divided into three stages in the reinforced concrete four-point bending test, namely ① the dominant action stage of tensioning, the initial loading step, the concentration of characteristic vectors is close to the average value of the tension class, ② the transition stage from tensioning to shearing, in which the high probability region gradually moves to the average value of the shearing class, ③ the failure stage, the shear crack control is performed during the final loading step, in which the most likely failure region is concentrated near the average value of the shear crack, the reason of the difference of the two loading modes and the material uniformity are different, and the proportion of the two types of cracks in the rock chamber test is still found to be different and the proportion of the maximum value of the acoustic emission behavior of the acoustic emission cracks in the rock chamber is found to be different from the initial loading stage, although the proportion of the acoustic emission crack is not obviously regular proportion of the loading stage, and the acoustic emission behavior is found to the maximum value of the acoustic emission behavior of the acoustic emission test.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (7)

1. An intelligent detection and identification method for a rock fracture mode based on an acoustic emission model is characterized by comprising the following steps:
step 1, arranging an acoustic emission system for testing acoustic emission parameters in a rock breaking process on a rock to be monitored;
step 2, inputting target characteristic data into a pre-trained signal recognition model, wherein the signal recognition model is obtained by training a training set of rock fracture acoustic emission in advance;
step 3, intelligently identifying the proportion of tension and shear crack development in the rock cracking process;
and 4, according to the corresponding relation between the waveform characteristics determined by the rock cracking acoustic emission signals and the rock cracking mode identification, providing a series of reliable detection threshold values for quantitatively formulating a rock disaster early warning scheme, and simultaneously providing an analysis method for deeply researching and identifying rock cracking instability precursor signal characteristics.
2. The intelligent detection and identification method for rock fracture patterns based on acoustic emission model is characterized in that in step 1, the acoustic emission system selects and measures the ringing count, duration, peak frequency and rise time in the rock acoustic signal to analyze the rock fracture process.
3. The method for intelligent detection and identification of rock cracking patterns based on acoustic emission model as claimed in claim 2, wherein in step 1, the method for collecting rock acoustic signals by the acoustic emission system is based on JCMS parameter analysis, i.e. the average frequency A of acoustic emission parameters is obtained by dividing the ringing count by the durationFDividing the rise time by the peak amplitude to obtain RAAnd then, the two groups of data are classified.
4. The method as claimed in claim 3, wherein in step 2, the preset training set of the signal recognition Model includes Gaussian Mixture Model (GMM) and Expectation Maximization (EM) algorithm.
5. The intelligent detection and identification method for rock rupture modes based on acoustic emission model as claimed in claim 4, characterized in that in step 2, according to AFAnd RAThe relation between the model and the model is used for analyzing tension and shear cracks, when tension and shear crack analysis is carried out, a Gaussian mixture model and an expected maximum algorithm are combined to serve as training models, the probability value of sampling and the closeness degree of the probability value of the model are observed to judge whether the model is fit or good, and the A is compared with the AFAnd RAThe relationship between them is intelligently detected and identified.
6. The intelligent detection and recognition method for rock rupture modes based on acoustic emission model as claimed in claim 5, wherein in step 2, the process is iterated for a plurality of times by adjusting the signal recognition model to make the new signal recognition model more adaptive to the probability value, and the updating is stopped and the model training is completed until the two probability values are very close, and the process is implemented by an algorithm:
calculating expected values of data through a Gaussian mixture model, wherein the Gaussian mixture model is a parameter probability density function and is expressed as weighting of Gaussian density of M components, and the expected values are maximized by continuously iterating to update the mean value mu and the standard deviation sigma of distribution until the two parameters change very little;
for D-dimensional measurement, training, the mixture density is defined as:
Figure FDA0002400222800000021
in the formula, ωiIn order to mix the weight values, the user can select the weight value,
Figure FDA0002400222800000022
is a single mode gaussian (normal) density,
Figure FDA0002400222800000023
is a feature vector;
the gaussian component density of each single mode is in the form of a D-variant gaussian function:
Figure FDA0002400222800000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002400222800000025
the vector is an average vector of Dx1, and the sigma i is a covariance matrix of DxD;
to let the mixed weight omegaiSatisfy the requirement of
Figure FDA0002400222800000026
The complete Gaussian mixture model should be formed by averaging vectors
Figure FDA0002400222800000027
The covariance matrix Σ i and the mixed weighting of all component densities M parameterize it λ, which is expressed by equation (3):
Figure FDA0002400222800000028
for a classification system based on a Gaussian mixture model, the goal of model training is to estimate the lambda of the parameters of the Gaussian mixture model so that the Gaussian mixture density and the feature vector
Figure FDA0002400222800000029
Determining the optimal estimate of λ;
maximum Likelihood estimation (ML) is used to estimate ωi
Figure FDA00024002228000000210
And Σ i, the maximum likelihood estimation estimate maximizes the probability of a gaussian mixture model given the training data, for a series of T training vectors
Figure FDA00024002228000000211
Given the independence between vectors, can be written as
Figure FDA00024002228000000212
This expression, as a non-linear function of λ, is computationally intractable to directly maximize (i.e. set the first derivative equal to zero and constrain the second derivative to be positive), considering the ML parameters obtained by iteration through the Expectation-maximization algorithm (EM for short).
7. The method for intelligent detection and identification of rock cracking patterns based on acoustic emission model as claimed in claim 6, wherein in step S2, the training process of expectation-maximization algorithm is an iterative process from the initial model λkInitially, a new model λ is then estimatedk+1Thus, there is p (X | λ)k+1)>p(X|λk) So that the new model becomes the initial model for the next iteration and the process is repeated until a certain convergence threshold is reached (e.g. the log likelihood is 1026), the algorithm consisting of two steps of expectation and maximization, which ensures a monotonic increase in the model's belief value, the result of the expectation step being the posterior probability for the i-th component, which is defined as the probability of state i, when the m-th mixture of gaussians results in state i
Figure FDA0002400222800000031
Given the kth re-estimated model λk
Figure FDA0002400222800000032
In the formula, ωi′
Figure FDA0002400222800000033
The distribution parameters are returned by equations (6), (7) and (8), respectively, with a maximization step:
Figure FDA0002400222800000034
Figure FDA0002400222800000035
Figure FDA0002400222800000036
the gaussian mixture model can classify structures having two types of crack patterns, i.e., tensile crack and shear crack (M is 2), such as rock and concrete, and the feature vector is used to classify the two types of crack patterns
Figure FDA0002400222800000037
(or measurement vector) is considered to be a two-dimensional vector (i.e., a vector of measurements)
Figure FDA0002400222800000038
) When there are T training vectors, the sequence
Figure FDA0002400222800000039
The two classes correspond to the pull and shear modes I ═ 1, 2, respectively, at which point the parameters of the gaussian mixture model (weight, mean and covariance matrices for each hidden class) are "estimated" and matched to the training eigenvectors
Figure FDA00024002228000000310
Are most closely matched.
CN202010144388.8A 2020-03-04 2020-03-04 Rock fracture mode intelligent detection and identification method based on acoustic emission model Pending CN111272883A (en)

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CN111812211A (en) * 2020-07-09 2020-10-23 武汉理工大学 RA-AF-E rock material brittle fracture crack classification method based on acoustic emission parameters
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